'curvature' originates from Latin, specifically the word 'curvatura', where the root 'curvus' meant 'bent'.

'curvature' came into English via Medieval Latin 'curvatura' (and related Old/Middle French forms) and eventually became the modern English word 'curvature'.

Initially it meant 'a bending' or 'a bent shape', but over time it evolved to include the sense 'degree or state of bending' and a more technical mathematical sense 'amount by which a curve deviates from a straight line'.